5 Answers
5

If you want to show some people you know about the "Tag der Deutschen Einheit" you can use "Herzlichen Glückwunsch zum Tag der Deutschen Einheit" like "Herzlichen Glückwunsch zum Geburtstag" or for an toast in a pub something like "Auf die Deutsche Einheit".

The suggestion of Em1 "Herzliche Grüße am Tag der Deutschen Einheit" or "Herzliche Grüße zum Tag der Deutschen Einheit" I would only write on a postcard, but wouldn't say it.

I disagree with TheBlastOne noting: "It is not celebrated among citizens." It depends if the person is political interested or not. As the Wikipedia site Tag der Deutschen Einheit (cited by diadiora in the comment) shows below the sections "Feierlichkeiten" and "Weitere Veranstaltungen" there are celebrations of that day.

Agree with @musiKk. Feel free to gain the rep. It's just not worth an answer for me; that does not mean that someone else may consider it differently.
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Em1Oct 2 '12 at 11:52

Funny thing is, it is impossible to disprove or prove that one wanted to post the answer independently of the comments posted previously...
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TheBlastOneOct 2 '12 at 12:51

Of course it is celebrated! Admittedly Not by many but there are people who have strong feelings for this holiday. In my eyes this is the most important national holiday in Germany (although I don't celebrate it).
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cgniederOct 20 '12 at 12:58

As others already wrote, Germans don't congratulate each other specifically on this day. However, one can derive what would most likely be what they would say if they did say anything special. Let's look at some common phrases:

Herzlichen Glückwunsch/Herzliche Glückwünsche: This phrase is used exclusively on personal special days/events ("Herzlichen Glückwunsch zum Geburtstag", "Herzliche Glückwünsche zum Namenstag", "Herzlichen Glückwunsch zur Beförderung", "Allen Gewinnern herzlichen Glückwunsch"). You don't use it on general holidays. Note also that this is the only case where you would use the word "gratulieren".

Alles Gute: This is used in those situations where also "Herzlichen Glückwunsch" can be used. Again, it's not used for general holidays.

Frohe(s)/Fröhliche(s): This is most often used with Christmas, Easter etc. ("Fröhliche Weihnachten", "Frohes Fest", "Frohe Ostern"), but "Froh" ist also used for New Year ("Frohes neues Jahr").

Ein gesegnete(s): Almost exclusively used for Christian holidays and New Year, and mostly by religious people ("Ein gesegnetes Weihnachten", "Ein gesegnetes Osterfest", "Ein gesegnetes neues Jahr").

So I'd say the most likely expression which Germans would use if they used any such expression at all on the 3rd of October is "Frohen Tag der deutschen Einheit" or "Fröhlichen Tag der deutschen Einheit".

As we can hear this afternoon what people say, here are my observations:

Almost all people say this:

"Schönen Feiertag morgen, Tschüss!"

What need to be said in addition:

Now, as the day is over and my answer was considered as "not useful" let me add that I haven't heard anybody say anything else. Definitely I did not hear any of the greetings mentioned in other answers with the exception of what TheBlastOne said, i.e. people did not say anything special.

If someone gratulated me for the Day of German Unity, I would think that there is something wrong with him. Either he is a nationalist, or he is mentally ill. I have never in my life heard anyone even mention that day except to note that there is a holiday.

In Germany, you wish people happy holidays on the big religious holidays (Christmas, Easter, Pentecost), and you congratulate them on personal occasions (birthday, wedding, promotion). You do not congratulate an individual for national events, especially not for something that is so generally disliked as the German Unity.

Mentally ill? Because one wants to celebrate the end of 40 years of Parteidiktatur? I heartily disagree!
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cgniederOct 20 '12 at 13:00

Where I live (Baden-Württemberg), I have never heard anyone mention that holiday except (a) to say that it is a work-free day or (b) to make fun of it. People (here, in this area) that are outspoken about such things are usually nationalists or mentally ill (preaching in the bus about politics, religion and illuminati). Maybe you live in a place where people actually celebrate this day, here they would prefer not to pay for east German highways and lazy Skinheads who are to stupid to find a job but clever enough to be proud of their heritage.
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user1914Oct 21 '12 at 15:48

I'm not going to continue this discussion although I'd have a few things to say. I shouldn't've started it in the first place as this is no place for a political discussion. Not even for one about German language if one reads the FAQ right... Have a nice day and regards from the center of Baden-Württemberg
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cgniederOct 21 '12 at 16:06